feat(frontend): slice 4 — migrate Dashboard + Applications to shadcn/Tailwind

Web UI rework.
- Migrate pages/Dashboard.tsx off @mui (shortcut CRUD dialogs, machine
  switcher, BackupDashboardWidget mount; shortcuts reuse ConfirmDialog/
  DialogFooter from slice 2)
- Migrate pages/Applications.tsx shell off @mui (tabs + library counts);
  keeps <Media/> child intact (Media.tsx still MUI, deferred to slice 7
  with its DataGrid)
- Behavioral tests for both pages

Gate: build + lint + test green.

frontend/src/pages/__tests__/Applications.test.tsx

@@ -0,0 +1,67 @@
+import { describe, it, expect, vi } from "vitest";
+import { render, screen } from "@testing-library/react";
+import { Applications } from "../Applications";
+
+// Applications still embeds the MUI Media child (migrated in slice 7). Mock it
+// so this slice-4 test stays focused on the migrated Applications shell and
+// does not pull the still-MUI DataGrid into the jsdom render.
+vi.mock("../Media", () => ({
+	Media: () => <div data-testid="media-child">Media</div>,
+}));
+
+vi.mock("react-router-dom", () => ({
+	useSearchParams: () => [new URLSearchParams(), vi.fn()],
+}));
+
+vi.mock("../../hooks/useSettings", () => ({
+	useMonitoringSettings: () => ({
+		data: [
+			{
+				id: "m1",
+				name: "Main",
+				enabled: true,
+				services: ["jellyfin"],
+			},
+		],
+	}),
+}));
+
+vi.mock("../../hooks/useDashboard", () => ({
+	useCounts: () => ({
+		data: { movies: 10, series: 5, episodes: 100 },
+	}),
+	useLibraries: () => ({
+		data: [
+			{ library: "Movies", total: 10, movies: 10, series: 0 },
+			{ library: "Shows", total: 5, movies: 0, series: 5 },
+		],
+	}),
+}));
+
+describe("Applications", () => {
+	it("renders the Jellyfin library counts grid and tabs, and keeps the Media child", () => {
+		render(<Applications />);
+
+		// Library stats header.
+		expect(screen.getByText("Library stats")).toBeInTheDocument();
+
+		// Counts: Total = 10 + 5 + 100 = 115, plus the per-type counts.
+		expect(screen.getByText("115")).toBeInTheDocument();
+		expect(screen.getByText("Episodes")).toBeInTheDocument();
+
+		// Library rows render their per-library totals (unique strings).
+		expect(
+			screen.getByText(/Total 10 · Movies 10 · Series 0/),
+		).toBeInTheDocument();
+		expect(
+			screen.getByText(/Total 5 · Movies 0 · Series 5/),
+		).toBeInTheDocument();
+
+		// Tabs present.
+		expect(screen.getByRole("tab", { name: "Jellyfin" })).toBeInTheDocument();
+		expect(screen.getByRole("tab", { name: "Nextcloud" })).toBeInTheDocument();
+
+		// The still-MUI Media child is rendered unchanged inside the Jellyfin tab.
+		expect(screen.getByTestId("media-child")).toBeInTheDocument();
+	});
+});